Introduction

Currently there are two major mathematical challenges in theoretical physics: understanding the origins of elementary particles, and understanding cosmology. The standard model of particle physics as well as the standard model of cosmology are successful theories that correctly describe a vast amount of data. Within the Mathematical Foundations we are interested in various kinds of theoretical models like, dark energy, dark matter, teleparallel gravity, modified gravity, Einstein-Cartan theory, brane-world models, inflation and loop quantum gravity. We are also working in classical general relativity and cosmology.

Dark Energy -- is a way to model the observed accelerated expansion of the universe with scalar fields or other forms of vacuum energy. One of our main interest is how we can learn more about dark energy with observations. We are also a member of the Dark Energy Survey (DES) team.

Modified Gravity -- Dark Energy is not the only possibilty to explain the observed accelerated expansion of the Universe. Modifactions to Einstein's general relativity on large scales could be a valid explanation for the observations. We are investigating how to constrain such theories and how to distinguish them from Dark Energy with observations. We are a member of the COSMOS supercomputing consortium and are using this machine to test comsological models.

Quantum Field Theory -- The Standard Model of particle physics is based on the quantum field theories QCD, describing the strong force, and the electroweak theory which contains QED. We work on application of QCD to the physics at particle colliders, in particular on the Large Hadron Collider (LHC) recently turned on at CERN, with special emphasis on the theoretical understanding of quark and gluon distributions and implications for collider experiments.

There is active collaboration with our UCL colleagues at the Mullard Space Science Laboratory (MSSL), especially their theory group. With Kinwah Wu and Houri Ziaeepur we meet regularly and are working on joint projects.